The Structure ofC*-Algebras Associated with Hyperbolic Dynamical Systems

We consider the stable, unstableC*-algebras and the Ruelle algebras associated to a mixing Smale space. In the case of a shift of finite type, these are the AF-algebras studied by W. Krieger and the (stabilized) Cuntz–Krieger algebras. In the general case, we show that the stable and unstable algebras are simple and amenable. We also show that the Ruelle algebras are simple, amenable, and purely infinite.